More precisely, they are equivalent for varieties of universal algebra, that is algebraic structures for which operations and axioms ( identities ) are defined without any restriction ( fields are not a variety, as the multiplicative inverse is defined either as a unary operation or as a property of the multiplication, which are, in both cases, defined only for nonzero elements ).
22.
Rather than dismissing it out of hand because of what you " think " the word " operator " implies, you could read the first sentence of the article, which states " a unary operation is an operation with only one operand, i . e . an operation with a single input " .-- Talk 15 : 56, 21 January 2009 ( UTC)
23.
E . g . a group theory is an algebraic theory because it has three functional terms : a binary operation " a * b ", a nullary operation " 1 " ( neutral element ), and a unary operation " x " ?! " x " 1 " with the rules of associativity, neutrality and inversion respectively.
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